Such balancing or measuring adapters are used for clamping a rotating component onto a balancing and/or measuring machine. A balancing machine having a balancing adapter of the type in question is known from DE 299 80 181 U1. It contains a main body having a centered receiving opening for the component to be clamped and a collet actuating unit, movable relative to the main body, for a collet chuck. In this known design, the collet chuck is fixedly mounted on the main body and is not movable axially relative thereto. The clamping tongues of the collet chuck are movable between a clamping and a release position by axially displacing the collet actuating unit. Additional centering elements, by which the components to be measured or balanced can be pre-tensioned radially, are often provided in the receiving opening region. In order to be able to release the clamped components after balancing or measurement, it also is necessary for the collet actuating unit to overcome the additional forces applied by the centering elements. For this purpose, the forces of the collet actuating unit must be increased, which can lead to jerky movements of the collet actuating unit. Since the axial movement of the collet actuating unit is generally also used to press the component out of the balancing or measuring adapter, there can be an undesired abrupt ejection of the components to be balanced or measured from the main body. This is particularly the case if the ejection is accomplished with compressed air.